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Unformatted text preview: MATH 191, Sections 1 and 3 Calculus I Fall 2007 Section 3.2: The Product and Quotient Rules Lets continue amassing shortcuts for computing derivatives. Weve now got rules for differentiating powers, as well as constant multiples, sums, and dif ferences of functions whose derivatives we already know. We even know the derivative of an exponential function f ( x ) = e x ! Whats missing? Well, lots. Products, for one. Lets examine d dx ( f g ), and see if we can get a nice formula. Sadly, its not what we might immediately expect. First, a motivating Example. Consider the numbers 4 and 7, whose product is 4 7 = 28. What happens if we add a very small quantity, say 1 , to 4, and another small quan tity, 2 , to 7, and then recompute the product? We now get (4 + 1 )(7 + 2 ) = . This expression represents the value to which the product 4 7 has been changed corresponding to a small change in those values. Whats most interesting here are those two crossterms in the middle. If we think of 4 and 7 as the valuesare those two crossterms in the middle....
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 Fall '07
 BAHLS
 Derivative, Quotient Rule

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